28278 + Interview Questions in Maths in Class 12

1.	int(dx)/((1+sinx)^((1)/(2)))=...+c
Answer» `sqrt(2)log\|TAN((3PI)/(8)-(x)/(4))\|` `sqrt(2)log\|"COSEC"((pi)/(8)+(x)/(2))-cot((pi)/(8)+(x)/(2))\|` `sqrt(2)log\|tan((pi)/(8)+(x)/(4))\|` `sqrt(2)log\|sec((pi)/(2)+(x)/(4))-tan((pi)/(2)+(x)/(4))\|` Answer :C

Discussion

2.	(d)/(dx) (tan^(n)x)= ……..
Answer» `"ntan^(N-1)X` `n tan^(n-1)x. SEC^(2)x` `n sec^(2N)x` `n tan^(n-1) x.sec^(n-1)x` Answer :B

Discussion

3.	int sqrt(1- sin 2x) dx=...... x in (0, (pi)/(4))
Answer» `-sinx+cosx+c` `sinx-cosx+c` `tanx+secx+c` `sinx+cosx+c` ANSWER :D

Discussion

4.	Let z_(1)" and "z_(2) be two complex numbers such that z_(1)z_(2)" and "z_(1)+z_(2) are real then
Answer» `z_(1)+z_(2)=0` `z_(1)-z_(2)=0` `z_(1)+barz_(2)=0` `z_(1)-barz_(2)=0` ANSWER :C

Discussion

5.	int f(x)dx=((logx)^(5))/(5)+c then f(x)=...
Answer» `(LOGX)/(4)` `((logx)^(4))/(x)` `((logx)^(3))/(5)` `((logx)^(6))/(6)` ANSWER :B

Discussion

6.	Let a, b and c be three non-zero vectors which are pairwise non-collinear. If a+3b is collinear with c and b+2c is collinear with a then a+3b+6cis
Answer» `a+c` a c `vec0` Solution :Given, `a + 3` b is collinearwith c. `rArr a + 3B= LAMBDA c "….."(i)` Also, `b + 3c`is collinearwith a. `rArr b + 2C = MUA "…"(ii)` From Eq. (i) we get `a + 3b + 6C= (lambda + 6) c "….."(ii)` From Eq. (ii), we get `a+ 3b +6 c= (1+3 mu) a"....."(iv)` On solvingEqs. (iii) and (iv) , we get `(lambda + 6) c = (1+3 mu) a` Since, a is not collinear with c. `rArr lambda + 6= 1 + 3 mu = 0` From Eq. (v), we get `a+ 3b + 6 c = 0`

Discussion

7.	If (1+3p)/(3), (1-p)/(4), (1-2p)/(2) are the probabilities of 3 mutually exclusive events then find the set of all values of p.
Answer» <P> ANSWER :`(1)/(3) LE p le (1)/(2)`

Discussion

8.	Students of two sections A and B of a class show the following performance in a test (##VIK_MAT_IIA_QB_C08_SLV_011_Q01.png" width="80%"> Which section of students has greater variability in performance ?
Answer» ANSWER :`RARR SIGMA _(2) = 9 `

Discussion

9.	Find the particular solution of thedifferential equation (1 + e^(2x))dy + (1 + y^(2))e^(x)dx = 0, given that y = 1 when x = 0
Answer» Answer :`TAN^(-1) y + tan^(-1)(e^(x)) = (pi)/(2)`

Discussion

10.	I : If O is the origin and if A(x_(1),y_(1)), B(x_(2), y_(2)) are two points then OAOBcos angleAOB=x_(1)x_(2)+ y_(1)y_(2) II. If O is the origin and if A(x_(1), y_(1)), B(x_(2), y_(2)) are two points then OAOB sin angleAOB=x_(1)x_(2)+y_(1)y_(2)
Answer» only I is TRUE only II is true both I and II are true NEITHER I nor II are true ANSWER :A

Discussion

11.	Find the number of functions from A to B where A={a_1,a_2,a_3,a_4,a_5} and B={b_1,b_2,b_3,b_4}such that b_1,b_2 must belong to the range of the function.
Answer» ANSWER :570

Discussion

12.	Find 6^(th) term of (3-4x^(2))^(-1)
Answer» SOLUTION :N/A

Discussion

13.	Evaluate the following integrals (ii)int_(pi/6)^(pi/3)(1)/(1+ root (3)(tan x))dx
Answer» ANSWER :`(PI)/(12)`

Discussion

14.	int (1)/(x^(4) 4 sqrt(x^(4) + 1))dx =
Answer» `(1)/(3)(1 + (1)/(x^(4)))^(3//4) + C ` `(-1)/(3)(1 + (1)/(x^(4)))^(3//4) + C ` `(2)/(3)(1 + (1)/(x^(4)))^(3//4) + C ` `(-2)/(3)(1 + (1)/(x^(4)))^(3//4) + C ` Answer :B

Discussion

15.	Letwe have a systemof linearinequations in twovariablesif the set of point (x,y)for whichall the inequations of thesystem holdtruethen the system are either or
Answer» NON EMPTY empty feasible REGION convex region ANSWER :B::D

Discussion

16.	If (y+5)^(2)=49, then which one of the following could be the value of (y+3)^(2)?
Answer» `1` `64` `81` `225` Answer :C

Discussion

17.	Find the shortest distance between the lines vecr =(8+3lambda) hati - (9 +16lambda) hatj+(10+7lambda)hatkand vecr= (15hati + 29hatj + 5hatk) + mu(3hati + 8hatj - 5hatk ).
Answer» ANSWER :14

Discussion

18.	Prove that the areas S_(0), S_(1), S_(2), .S_(2),. S_(3),….., bounded by the x-axis and half-waves o the curve y= e^(-alpha x) sin beta x, x ge 0, from a geometric progression with the common ratio q=( e^(alpha x)/(beta))
Answer» ANSWER :`E^(-ALPHA pi//beta)`

Discussion

19.	A circular path is 50 m. wide. The angle of elevation of the top of a pole at the centre of the circular park at a point on the outer circle is 45^(@). The height of the pole is
Answer» `(50 cos alpha)/(cos alpha-sin alpha)` `(50 sin alpha)/(sin alpha-cos alpha)` `(50)/(cos alpha-sin alpha)` `(50)/(cos alpha+sin alpha)` ANSWER :B

Discussion

20.	Consider an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a gt b) and a circle x^(2)+y^(2)=a^(2). A tangent is drawn at any point on the circleand a point is chosen on this tangent from which pair of tangents are drawn to the ellipse. If the chord of contant passes through a fixed point (x_(1),y_(1)) then prove that x_(1)^(2)+(a^(4)/(b^(4))y_(1)^(4)=a^(2)
Answer» ANSWER :`H^(2)+K^(2)=a^(2)`

Discussion

21.	If int(dx)/((x-sqrt(x^(2)-1)))=Ax^(3)+Bx^(2)+Cx+D(x^(2)-1)^(3//2)+E, then
Answer» `A=(2)/(3),B=0,C=-1` `A=(1)/(3),B=0,D=(2)/(3)` `A=D=(2)/(3),B=0,C=-2` NONE of these Answer :A

Discussion

22.	Evaluate: int_(0)^(2)e^(x)dx as a limit of sum.
Answer» ANSWER :`=E^(2)-1`

Discussion

23.	When 22.4 litres of H_(2)(g)is mixed with 11.2 litres of CI_(2)(g), eacg at STP, the moles of HCI(g) formed is equal to :-
Answer» 0.5 MOL of HCI (g) 1.5 mol of HCI (g) 1 mol of HCI (g) 2 mol of HCI (g) ANSWER :A

Discussion

24.	Assertion (A) : The number of ways in which 6 persons can sit around a round table is 120. Reason (R) : The number of circular permutaions of n different things taken all at a time in one direction is ((n-1)!)/(2) The correct answer is
Answer» Both A and R are true and R is the CORRECT EXPLANATION of A Both A and R are true but R is not correct explanation of A A is true but R is false A is false but R is true Answer :B

Discussion

25.	I : (C_1)/(C_2) + 2 (C_2)/(C_1) + 3. (C_3)/(C_2) +…...+n. (C_n)/( C_(n-1))= (n(n+1))/(2) II : C_0 + (C_1)/(2) + (C_2)/(3) + …. +( C_n)/( n+1) = (2^(n+1) - 1)/( n+1)
Answer» only I is true only II is true both I and II are true neither I nor II true Answer :C

Discussion

26.	Find derivatives of the following function.2^(2^x)
Answer» SOLUTION :`y=2^((2X))` `RARR` In `y =2^xcdotIn 2` `rArr1/ydy/dx=2^xcdotIn2cdotIn2` `rArr dy/dx=2^((2^x)cdot2^xcdot(IN2)^2

Discussion

27.	Find the coefficient of x^6 in (1 - 3x)^(-2//5)
Answer» ANSWER :`(2.7.12…….27)/(6!) (3/5)^6`

Discussion

28.	Evaluate the integrals by using substitution int_(0)^(2)(dx)/(2x+4-x^(2))
Answer» ANSWER :`

Discussion

29.	When a coin is tossed n times if the probability for getting 6 heads is equal to the probability for getting 8 heads then find the value of n.
Answer» ANSWER :14

Discussion

30.	Using Cofactors of elements of third column , evaluateDelta=\|{:(1,x,yz),(1,y,zx),(1,z,xy):}\|
Answer» ANSWER :(x-y)(y-z)(z-x)

Discussion

31.	A point O is the centre of a circle circumscribed about a triangle ABC. Then, O vec A sin 2 A + O vec Bsin 2 B + O vec Csin 2 Cis equal to
Answer» `(O VEC a + O vec B + O vec C ) sin 2 A ` `3 vec(OG), ` where G is the centroid of triangle ABC `vec 0` none of these Answer :C

Discussion

32.	The odds against a certain event is 5 : 2 and the odds in favour of another event is 6 : 5.If the both the events are independent, then the probability that at least one of the events will happen is
Answer» `50/77` `52/77` `25/88` `63/88` ANSWER :B

Discussion

33.	The points at which the tangents to the curve y=x^(3)-12x+18 are parallel to X-axis are :
Answer» `(2,-2), (-2,-34)` `(2,34),(-2,0)` `(0,34),(-2,0)` `(2,2),(-2,34)` ANSWER :D

Discussion

34.	int_(0)^(pi/4) (sinx + cosx)/(3+sin2x) dx=
Answer» `(1)/(2) LOG 3` `log 2` `log 3` `(1)/(4) log 3` ANSWER :D

Discussion

35.	India and Pakistan play a series of 'n' one day matches and probability than India wins a match against Pakistan is (1)/(2) If 'n' is not fixed and series ends when any one of the team completes its 4^(th) win then probability that India wins the series is
Answer» `(4)/(2^(7))` `(1)/(2^(7))` `(1)/(2)` None Solution :(i)REQUIRED PROBABILITY `= (1)/(2)`. (II) Required probability `= ((1)/(2))^(3)+((1)/(2))^(4)+((1)/(2))^(4)+((1)/(2))^(4)+((1)/(2))^(4)-((1)/(2))^(7)=(47)/(2^(7))`.

Discussion

36.	The variance of the following data is
Answer» 48.5 45.8 54.8 58.4 Answer :B

Discussion

37.	India and Pakistan play a series of 'n' one day matches and probability than India wins a match against Pakistan is (1)/(2) IF n = 7 , then probabilitythat India wins atleast three consecutive matches is
Answer» `(17)/(2^(6))` `(47)/(2^(7))` `(47)/(2^(6))` None Solution :(i)REQUIRED probability `= (1)/(2)`. (ii) Required probability `= ((1)/(2))^(3)+((1)/(2))^(4)+((1)/(2))^(4)+((1)/(2))^(4)+((1)/(2))^(4)-((1)/(2))^(7)=(47)/(2^(7))`.

Discussion

38.	Eight athletes compete in a race in which a gold, a silver and a bronze medal will be awarded to the top three finishers, in that order. {:("Quantity A","Quantity B"),("The number of ways in which",8xx3!),("the medals can be awarded",):}
Answer» ANSWER :QUANTITY A is GREATER.

Discussion

39.	Show that the function f given byf(x) ={:( x^(2)+5, if xne 0), (3, if x = 0):}
Answer» Solution :The function is defined at x =0 its VALUE at x =0 is 3 when `x ne 0`, the function is given by a polynomial, Hence, ` underset(x to 0) lim F(x) = underset(x to 0)lim x^(2)+5 =0^(2) + 5=5 ` Since the limit does notcoincide with f(0) , the function is not continuous at x =0, As well, x =0 is the only point of discontinuity .

Discussion

40.	Find the angle between the lines whose direction cosines are given by the equation l + m + n = 0 and l^2 + m^2 - n^2 = 0.
Answer» ANSWER :`120^@`

Discussion

41.	If (3/2+i(sqrt3)/2)=3^(25)(x+iy), where x and y are real then ordered pair (x,y) is
Answer» (- 3, 0) (0,3) (0, -3) `(1/2,(SQRT3)/2)` ANSWER :D

Discussion

42.	Differentiate.x^(sqrtx)
Answer» SOLUTION :`y=X^(SQRTX)` In `y=sqrtxcdotInxrArr1/2dy/dx=1/(2sqrtx)Cdot In x+sqrtxcdot1/x` `rArr dy/dx=x^(sqrtx){(Inx)/(2sqrtx)+1/sqrtx}=x^(sqrtx)(Inesqrtx)/sqrtx`

Discussion

43.	Evaluate : (i) int_(0)^(4)[x]^(2) dx (where []denotes greatestinteger function) (ii) int_(0)^(pi)sqrt(1+sin2x)dx , (iii) int_(0)^(2)f(x)dx where f(x)-[{:(2x+1, 0lexlt1),(3x^(2),1lexle2):} (iv) int_(0)^(4)\|x^(2)+4x+3\|dx , (v) int_(0)^(oo)[cot^(1)x]dx (where [] denotes greatest integerfunction) (vi) int_(-5)^(5)\|x+2\|dx , (vii) int_(-1)^(1)[cos^(-1)x]dx (where [*] denotes greatest integerfunction)
Answer» SOLUTION :N//A

Discussion

44.	-2[(1)/(8)+(1)/(64)+(1)/(384)+…..oo]=
Answer» `log_(E )(1//4)` `log_(e )(1//2)` `log_(e )(3//4)` `log_(e )(3//8)` ANSWER :C

Discussion

45.	Show that the normal to the curve 5x^(5)-10x^(3)+x+2y+6=0 at P(0,-3) intersects the curve again in two points. Also find these points.
Answer» ANSWER :`(1,-1),(-1,-5)`

Discussion

46.	If n = 12 m (m in N),prove that .^(n)C_(0)- (.^(n)C_(2))/((2+sqrt(3))^(2)) + (.^(n)C_(4))/((2+sqrt(3))^(4))-(.^(n)C_(n))/((2+sqrt(3))^(6)) + "....." = (-1)^(m) ((2sqrt(2))/(1+sqrt(3)))^(n)
Answer» SOLUTION :`.(N)C_(0)-(.^(n)C_(2))/((2+sqrt(3))^(2))+(.^(n)C_(4))/((2+sqrt(3))^(4))-(.^(n)C_(6))/((2+sqrt(3))^(6))+"...."` = Real part of`(1+(i)/(2sqrt(3)))^(n)` = Real part of `(1+i(2-sqrt(3))^(n)` = Real part of `(1+ I tan'(pi)/(12))^(n)` = Real part of `((cos'pi/12+isin'(pi)/(12))^(n))/(cos^(n)'(pi)/(12))` = Realpart of `((cos' (npi)/(12)+isin'(npi)/(12)))/(cos^(n)'(pi)/(12))` ` = (cos'(npi)/(12))/(cos^(n)'(pi)/(12)) = (cos mpi)/(cos^(n)'(pi)/(12))` ` = (-1)^(m)((2sqrt(2))/(1+sqrt(3)))^(n) , [:' cos'(pi)/(12) = (sqrt(3) + 1)/(2sqrt(2))]`

Discussion

47.	Find the middle term in the expansion of the (a/b+b/a)^6.
Answer» Solution :`(a/b+b/a)^6`Here there is only ONE MIDDLE TERM i.e. the 4th term. ` therefore` 4th term i.e. (3+1)th term in the expansion of `(a/b+b/a)^6` is `"^6C_3 (a/b)^6-3(b/a)^3` `6!/3!3!(a/b)^3(b/a)^3` = 6.5.4/6 = 20

Discussion

48.	If a normal chord of the parabola y^(2)=4xmakes an angle of 45^(@) with the axis of the parabola then its length is
Answer» 8 `8 SQRT(2)` 4 `4sqrt(2)` Answer :B

Discussion

49.	The tangent at 'p' on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 cuts the major axis in T and PN is the perpendicular to the x-axis, C being centre then CN.CT =
Answer» ANSWER :`a^(2)`

Discussion

50.	Let S=(1)/(1xx3xx5)+(1)/(3xx5xx7)+(1)/(5xx7xx9)+(1)/(7xx9xx11)+…" upto "oo then 3S=
Answer» ANSWER :0.25

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

int(dx)/((1+sinx)^((1)/(2)))=...+c

(d)/(dx) (tan^(n)x)= ……..

int sqrt(1- sin 2x) dx=...... x in (0, (pi)/(4))

Let z_(1)" and "z_(2) be two complex numbers such that z_(1)z_(2)" and "z_(1)+z_(2) are real then

int f(x)dx=((logx)^(5))/(5)+c then f(x)=...

Let a, b and c be three non-zero vectors which are pairwise non-collinear. If a+3b is collinear with c and b+2c is collinear with a then a+3b+6cis

If (1+3p)/(3), (1-p)/(4), (1-2p)/(2) are the probabilities of 3 mutually exclusive events then find the set of all values of p.

Students of two sections A and B of a class show the following performance in a test (##VIK_MAT_IIA_QB_C08_SLV_011_Q01.png" width="80%"> Which section of students has greater variability in performance ?

Find the particular solution of thedifferential equation (1 + e^(2x))dy + (1 + y^(2))e^(x)dx = 0, given that y = 1 when x = 0

I : If O is the origin and if A(x_(1),y_(1)), B(x_(2), y_(2)) are two points then OA*OB*cos angleAOB=x_(1)x_(2)+ y_(1)y_(2) II. If O is the origin and if A(x_(1), y_(1)), B(x_(2), y_(2)) are two points then OA*OB * sin angleAOB=x_(1)x_(2)+y_(1)y_(2)

Find the number of functions from A to B where A={a_1,a_2,a_3,a_4,a_5} and B={b_1,b_2,b_3,b_4}such that b_1,b_2 must belong to the range of the function.

Find 6^(th) term of (3-4x^(2))^(-1)

Evaluate the following integrals (ii)int_(pi/6)^(pi/3)(1)/(1+ root (3)(tan x))dx

int (1)/(x^(4) 4 sqrt(x^(4) + 1))dx =

Letwe have a systemof linearinequations in twovariablesif the set of point (x,y)for whichall the inequations of thesystem holdtruethen the system are either or

If (y+5)^(2)=49, then which one of the following could be the value of (y+3)^(2)?

Find the shortest distance between the lines vecr =(8+3lambda) hati - (9 +16lambda) hatj+(10+7lambda)hatkand vecr= (15hati + 29hatj + 5hatk) + mu(3hati + 8hatj - 5hatk ).

Prove that the areas S_(0), S_(1), S_(2), .S_(2),. S_(3),….., bounded by the x-axis and half-waves o the curve y= e^(-alpha x) sin beta x, x ge 0, from a geometric progression with the common ratio q=( e^(alpha x)/(beta))

A circular path is 50 m. wide. The angle of elevation of the top of a pole at the centre of the circular park at a point on the outer circle is 45^(@). The height of the pole is

If int(dx)/((x-sqrt(x^(2)-1)))=Ax^(3)+Bx^(2)+Cx+D(x^(2)-1)^(3//2)+E, then

Evaluate: int_(0)^(2)e^(x)dx as a limit of sum.

When 22.4 litres of H_(2)(g)is mixed with 11.2 litres of CI_(2)(g), eacg at STP, the moles of HCI(g) formed is equal to :-

Assertion (A) : The number of ways in which 6 persons can sit around a round table is 120. Reason (R) : The number of circular permutaions of n different things taken all at a time in one direction is ((n-1)!)/(2) The correct answer is

I : (C_1)/(C_2) + 2 (C_2)/(C_1) + 3. (C_3)/(C_2) +…...+n. (C_n)/( C_(n-1))= (n(n+1))/(2) II : C_0 + (C_1)/(2) + (C_2)/(3) + …. +( C_n)/( n+1) = (2^(n+1) - 1)/( n+1)

Find derivatives of the following function.2^(2^x)

Find the coefficient of x^6 in (1 - 3x)^(-2//5)

Evaluate the integrals by using substitution int_(0)^(2)(dx)/(2x+4-x^(2))

When a coin is tossed n times if the probability for getting 6 heads is equal to the probability for getting 8 heads then find the value of n.

Using Cofactors of elements of third column , evaluateDelta=|{:(1,x,yz),(1,y,zx),(1,z,xy):}|

A point O is the centre of a circle circumscribed about a triangle ABC. Then, O vec A sin 2 A + O vec Bsin 2 B + O vec Csin 2 Cis equal to

The odds against a certain event is 5 : 2 and the odds in favour of another event is 6 : 5.If the both the events are independent, then the probability that at least one of the events will happen is

The points at which the tangents to the curve y=x^(3)-12x+18 are parallel to X-axis are :

int_(0)^(pi/4) (sinx + cosx)/(3+sin2x) dx=

India and Pakistan play a series of 'n' one day matches and probability than India wins a match against Pakistan is (1)/(2) If 'n' is not fixed and series ends when any one of the team completes its 4^(th) win then probability that India wins the series is

The variance of the following data is

India and Pakistan play a series of 'n' one day matches and probability than India wins a match against Pakistan is (1)/(2) IF n = 7 , then probabilitythat India wins atleast three consecutive matches is

Eight athletes compete in a race in which a gold, a silver and a bronze medal will be awarded to the top three finishers, in that order. {:("Quantity A","Quantity B"),("The number of ways in which",8xx3!),("the medals can be awarded",):}

Show that the function f given byf(x) ={:( x^(2)+5, if xne 0), (3, if x = 0):}

Find the angle between the lines whose direction cosines are given by the equation l + m + n = 0 and l^2 + m^2 - n^2 = 0.

If (3/2+i(sqrt3)/2)=3^(25)(x+iy), where x and y are real then ordered pair (x,y) is

Differentiate.x^(sqrtx)

-2[(1)/(8)+(1)/(64)+(1)/(384)+…..oo]=

Show that the normal to the curve 5x^(5)-10x^(3)+x+2y+6=0 at P(0,-3) intersects the curve again in two points. Also find these points.

If n = 12 m (m in N),prove that .^(n)C_(0)- (.^(n)C_(2))/((2+sqrt(3))^(2)) + (.^(n)C_(4))/((2+sqrt(3))^(4))-(.^(n)C_(n))/((2+sqrt(3))^(6)) + "....." = (-1)^(m) ((2sqrt(2))/(1+sqrt(3)))^(n)

Find the middle term in the expansion of the (a/b+b/a)^6.

If a normal chord of the parabola y^(2)=4xmakes an angle of 45^(@) with the axis of the parabola then its length is

The tangent at 'p' on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 cuts the major axis in T and PN is the perpendicular to the x-axis, C being centre then CN.CT =

Let S=(1)/(1xx3xx5)+(1)/(3xx5xx7)+(1)/(5xx7xx9)+(1)/(7xx9xx11)+…" upto "oo then 3S=

I : If O is the origin and if A(x_(1),y_(1)), B(x_(2), y_(2)) are two points then OAOBcos angleAOB=x_(1)x_(2)+ y_(1)y_(2) II. If O is the origin and if A(x_(1), y_(1)), B(x_(2), y_(2)) are two points then OAOB sin angleAOB=x_(1)x_(2)+y_(1)y_(2)